Numbers with Non-increasing Digits
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Note that this is a practice quiz. This problem will be discussed in the next video, but we encourage you to try to solve it yourselves first.
How many four-digit numbers are there such that their digits are non-increasing, that is each next digit is not greater than the previous one? Three-digit numbers are also four-digit, they just start with 0.
This is correct! To fix such a number it is sufficient and enough to pick unordered subset of four numbers from 0 to 9. Then they can be ordered into a non-increasing order in a unique way. Since there might be equal digits in our number, repetitions are allowed. Thus we are dealing with combinations of size 4 out of 10 options with repetitions.
See the next video for discussion.